Unicity of meromorphic mappings / Pei-Chu Hu, Ping Li, Chung-Chun Yang.

Format:

Book

Author/Creator:

Hu, Pei-Chu.

Contributor:

Li, Ping, 1962 October 5-

Yang, Chung-Chun, 1942-

Rosengarten Family Fund.

Series:

Advances in complex analysis and its applications ; v. 1.

Advances in complex analysis and its applications ; v. 1

Language:

English

Subjects (All):

Functions, Meromorphic.

Physical Description:

ix, 467 pages ; 25 cm.

Place of Publication:

Dordrecht ; Boston : Kluwer Academic Publishers, 2003.

Summary:

This book introduces value distribution theory starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic mappings from parabolic manifolds into projective spaces. Then the unicity theory of meromorphic functions or mappings is discussed systematically and the discussion also covers value distribution theory of algebroid functions of several variables and its applications in unicity theory. Audience: Graduate students and researchers involved in the fields of analysis, complex function theory of one or several variables, value distribution theory and analysis on complex manifolds.

Contents:

1 Nevanlinna theory 1

1.1 Parabolic manifolds and Hermitian geometry 1

1.2 The first main theorem 9

1.3 Growths of meromorphic functions 19

1.4 The lemma of logarithmic derivative 31

1.5 Growth estimates of Wronskians 42

1.6 The second main theorem 47

1.7 Degenerate holomorphic curves 53

1.8 Value distribution of differential polynomials 63

1.9 The second main theorem for small functions 76

1.10 Tumura-Clunie theory 86

1.11 Generalizations of Nevanlinna theorem 101

1.12 Generalizations of Borel theorem 109

2 Uniqueness of meromorphic functions on C 119

2.1 Functions that share four values 119

2.2 Functions that share three values CM 133

2.3 Functions that share pairs of values 144

2.4 Functions that share four small functions 150

2.5 Functions that share five small functions 157

2.6 Uniqueness related to differential polynomials 163

2.7 Polynomials that share a set 191

2.8 Meromorphic functions that share the same sets 194

2.9 Unique range sets 199

2.10 Uniqueness polynomials 205

3 Uniqueness of meromorphic functions on C[superscript m] 211

3.1 Technical lemmas 211

3.2 Multiple values of meromorphic functions 220

3.3 Uniqueness of differential polynomials 223

3.4 The four-value theorem 229

3.5 The three-value theorem 234

3.6 Generalizations of Rubel-Yang's theorem 243

3.7 Meromorphic functions sharing one value 254

3.8 Unique range sets of meromorphic functions 262

3.9 Unique range sets ignoring multiplicities 274

3.10 Meromorphic functions of order [less than sign] 1 284

3.11 A note on the abc-conjecture 293

3.12 A note on Hall's conjecture 301

4 Uniqueness of meromorphic mappings 309

4.1 Notes on the first main theorem 309

4.2 The first main theorem for line bundles 316

4.3 The second main theorem for line bundles 325

4.4 Uniqueness of meromorphic mappings into P[superscript n] 333

4.5 Finiteness theorems 340

4.6 General meromorphic mappings 347

4.7 Dependence theorems 353

4.8 Propagation theorems 365

4.9 Uniqueness dealing with multiple values 374

5 Algebroid functions of several variables 379

5.2 Techniques of value distribution 385

5.3 The second main theorem 389

5.4 Algebroid reduction of meromorphic mappings 395

5.5 The growth of branching divisors 406

5.6 Reduction of Nevanlinna theory 412

5.7 Generalizations of Malmquist theorem 422

5.8 Uniqueness problems 430

5.9 Multiple values of algebroid functions 437.

Notes:

Includes bibliographical references (pages 441-459) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

1402012195

OCLC:

51770249